Sources "close to the HS2 panel" are quoted as saying the proposal is "one of 13" options being considered by the review panel which is being led by former HS2 chairman Douglas Oakervee.
It has been suggested that the panel is mulling alternatives to the proposed HS2 route, which splits into east and west legs after Birmingham.
One of the options is said to be for trains from London to run thorough Birmingham to Manchester and then Leeds. This would create 20-minute journey times between Leeds and Manchester, instead of the current average of one hour and 11 minutes.
According to a report in The Sunday Times, the option would see the scrapping of the proposed eastern line, which goes to Leeds via Toton - a new station between Nottingham and Derby - generating a £10bn saving.
A report published last month suggested that the costs of delivering HS2 could soar by more than £20bn, to £88bn.
A spokesman at the Department for Transport said: “The independent review into HS2, led by Douglas Oakervee with Lord Berkeley as deputy and a panel of advisers, will provide the department with clear advice on how and whether the project should proceed.
“We are not going to pre-empt or prejudice this work with a running commentary on the review’s progress.”
The latest reports follow claims a week ago that the review panel was considering recommending that the section of the rail route to Leeds and Sheffield is scrapped to save money.
The suggestion prompted a furious backlash from some of the region’s politicians.
Councillor Judith Blake, leader of Leeds Council and transport lead for the West Yorkshire Combined Authority, warned of "grave long-term consequences" for the economy of the North and East of the UK if the eastern leg of HS2 is not delivered in full.
During separate visits to Yorkshire in the last week, Labour leader Jeremy Corbyn said the axing of HS2 in Yorkshire would be an “awful” decision, while Northern Powerhouse Minister Jake Berry admitted he would be “disappointed” if the Leeds and Sheffield section of HS2 is dropped.
According to today's reports, no decision has been made on the panel's recommendations to the Government.